curve #240

y² + xy = x³ − x² − 29015852737941337052556x + 1950033817928958623296270251397996

a-invariants: [1, -1, 0, -29015852737941337052556, 1950033817928958623296270251397996]
c-invariants: [1392760931421184178522697, -1684829218684352826336582168404516421]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 4408842402542882663229878258486367642610523089350038242434310458
discriminant (Δ): -79279804082526116050199670844101862949422426192692387675453770655756 ★ record for rank ≥ 19
Faltings height: 11.8074 ★ record for rank ≥ 19
naive height: 166.8295 ★ record for rank ≥ 19
primes of bad reduction: 2, 3, 37, 700537, 18100151, 522080015783791737432359443783998886705332553199
regulator: 3358763679517923421.250400962994444783072161684480141170565001749810867504768
submitted by: David Renshaw
submitted at: 2026-06-27 20:28:11 UTC
last updated: 2026-07-01 22:30:41 UTC

(189487870172, -57057674297755018)
(353802982691, -189662971158293806)
(355325104871/4, 68578732568253475/8)
(96203780642, -6998703778466524)
(91779544109, 7750803665126231)
(-109930517796, -61735527520602634)
(1950621330926, -2714281024184132410)
(241118393681, 94720196271901040)
(438116835554, -270800205716126470)
(485397239411, -319735282350834910)
(4057642908764/49, -3680012902401856630/343)
(558660770147, -400124108256470254)
(11908790775, 40077157054716614)
(70449696131/4, 304048098933340693/8)
(12274003974266/121, -9457397708951999060/1331)
(310042114371/4, 103281470730117533/8)
(546843209204/25, -4551468576776888702/125)
(1033674110941/9, 310818670187071052/27)
(7352771837441/169, -60963589848814834888/2197)

Generated by rational Mestre (u,v) discriminant search: u=-3, v=-1/2, T=2229/16; exact abs-discriminant frontier triage.

last edited by David Renshaw at 2026-06-27 20:28:11 UTC · history